Matrix method analysis of quantum Hall effect device connections

The modelling of electrical connections of single or several multiterminal quantum Hall effect (QHE) devices is relevant for electrical metrology: it is known in fact that certain particular connections allow (i) the realization of multiples or fractions of the quantized resistance or (ii) the rejection of stray impedances so that the configuration maintains the status of quantum standard. Ricketts–Kemeny and Delahaye equivalent circuits are known to be accurate models of the QHE: however the numerical or analytical solution of electrical networks including these equivalent circuits can be difficult. In this paper we introduce a method of analysis based on the representation of a QHE device by means of the indefinite admittance matrix: external connections are then represented with another matrix easily written by inspection. Some examples including the solution of double- and triple-series connections are shown.